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First Order Second Order Laplace Transforms Additional Topics Applications, Practice
Separation of Variables
Linear
Integrating Factors (Linear)
Substitution
Exact Equations
Integrating Factors (Exact)
Linear
Constant Coefficients
Substitution
Reduction of Order
Undetermined Coefficients
Variation of Parameters
Polynomial Coefficients
Cauchy-Euler Equations
Chebyshev Equations
Laplace Transforms
Unit Step Function
Unit Impulse Function
Square Wave
Shifting Theorems
Solve Initial Value Problems
Classify Differential Equations
Fourier Series
Slope Fields
Wronskian
Existence and Uniqueness
Boundary Value Problems
Euler's Method
Inhomogeneous ODE's
Resonance
Partial Differential Equations
Linear Systems
Exponential Growth/Decay
Population Dynamics
Projectile Motion
Chemical Concentration
Fluids (Mixing)
Practice Problems
Practice Exam List
Exam A1
Exam A3
Exam B2

You CAN Ace Differential Equations

17calculus > differential equations > various topics

Topics You Need To Understand For This Page

Differential Equations Alpha List

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Various Differential Equations Topics

This page contains several differential equations topics that are not discussed in detail but we provide some overview information and maybe a video or two, as well as links to other pages with more in-depth information, if we have any. We may expand these topics as a later date but, for now, this will get you started. Here is a list of topics on this page.

Basic Topics

 

Advanced Topics

Existence and Uniqueness

Partial Differential Equations

Boundary Value Problems

Linear Systems

Euler's Method

Inhomogeneous ODEs

Resonance

Existence and Uniqueness

Here is a discussion of the Lipschitz condition, which is related to whether a differential equation has a solution and, if so, whether the solution is unique.

Dr Chris Tisdell - Lipschitz Condition

Boundary Value Problems

Here are three videos related to boundary value problems.

Dr Chris Tisdell - advanced differential equations and boundary value problems

Dr Chris Tisdell - how to determine eigenvalues of a boundary value problem

Dr Chris Tisdell - D'alembert's approach for boundary value problems

Euler's Method

MIT OCW - Title: Lec 2 | MIT 18.03 Differential Equations, Spring 2006;
Topics: Euler's Numerical Method for y'=f(x,y) and its Generalizations

Inhomogeneous ODEs

MIT OCW - Title: Lec 13 | MIT 18.03 Differential Equations, Spring 2006
Topics: Finding Particular Sto Inhomogeneous ODE's: Operator and Solution Formulas Involving Exponentials

Resonance

MIT OCW - Title: Lec 14 | MIT 18.03 Differential Equations, Spring 2006
Topic: Interpretation of the Exceptional Case: Resonance

Partial Differential Equations

Here are two videos related to pde's using the method of characteristics. We highly recommend this guy's videos.

Dr Chris Tisdell - This first video introduces the topic and gives some examples.

Dr Chris Tisdell - This second video gives more detail and another example.

Linear Systems

Dr Chris Tisdell - How to solve systems of ODEs without matrices

Dr Chris Tisdell - Basic solution form to systems of differential equations

Dr Chris Tisdell - How to solve systems of differential equations

PatrickJMT - Homogeneous Systems of Linear Equations - Trivial and Nontrivial Solutions, Part 1

PatrickJMT - Homogeneous Systems of Linear Equations - Trivial and Nontrivial Solutions, Part 2

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